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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
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    Inverse View

    It is not the case that A coNP witness must be both unique-enough to be convincing and polynomially bounded in size; the prime factorization of n can require exponentially many bits relative to log n when n has many small factors.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.A factorization witness for n only needs to list factors once each; even with many small primes, encoding k factors takes O(k log n) bits, which is polynomial in log n when k is bounded by log n.
      ?

      Think about whether this reason is strong or weak

    • 2.The claim conflates worst-case encoding with necessity; a compact representation (exponent-prime pairs) avoids the exponential blowup described.
      ?

      Think about whether this reason is strong or weak

    • 3.If factorization witnesses were unpolynomially sized, coNP ≠ NP would follow trivially; this contradicts that the P vs NP question remains open, suggesting the premise oversimplifies the structural issue.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.coNP witnesses verify negations; a factorization's bit-length is determined by the multiplicands themselves, not the number being tested.
      ?

      Think about whether this reason is strong or weak

    • 2.Numbers with many small prime factors (e.g., 2·3·5·7·...) have factorizations requiring exponentially more bits than log n, which is mathematically sound.
      ?

      Think about whether this reason is strong or weak

    • 3.Polynomial verification requires witnesses whose size is polynomially bounded in input length; exponential-bit factorizations violate this constraint fundamentally.
      ?

      Think about whether this reason is strong or weak

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